
Applications of the Topological Derivative Method
Springer (Publisher)
Published on 12. January 2019
Book
Hardback
XIV, 212 pages
978-3-030-05431-1 (ISBN)
Description
The book presents new results and applications of the topological derivative method in control theory, topology optimization and inverse problems. It also introduces the theory in singularly perturbed geometrical domains using selected examples. Recognized as a robust numerical technique in engineering applications, such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena, the topological derivative method is based on the asymptotic approximations of solutions to elliptic boundary value problems combined with mathematical programming tools. The book presents the first order topology design algorithm and its applications in topology optimization, and introduces the second order Newton-type reconstruction algorithm based on higher order topological derivatives for solving inverse reconstruction problems. It is intended for researchers and students in applied mathematics and computational mechanics interested in the mathematical aspects of the topological derivative method as well as its applications in computational mechanics.
Reviews / Votes
"The book is well written, and the examples treated are carefully motivated. The references are up-to-date. The material presented in the book requires good mathematical background, so that the book could be used, as usefull reference, for researchers and graduate students that are working in the optimization theory."(Teodor Atanackovic, zbMATH 1460.74001, 2021)"The book under review provides an excellent overview of historical and current developments in the field and, at the same time, is a very good introduction to readers familiar with linear elliptic equations and variational inequalities. . In all chapters, a thorough literature discussion is provided along with a detailed discussion of open problems." (Guenter Leugering, Mathematical Reviews, October, 2019)
More details
Series
Edition
2019 ed.
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
53 s/w Abbildungen, 9 farbige Abbildungen
XIV, 212 p. 62 illus., 9 illus. in color.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 18 mm
Weight
512 gr
ISBN-13
978-3-030-05431-1 (9783030054311)
DOI
10.1007/978-3-030-05432-8
Schweitzer Classification
Other editions
Additional editions

Antonio André Novotny | Jan Sokolowski | Antoni Zochowski
Applications of the Topological Derivative Method
E-Book
12/2018
1st Edition
Springer
€139.09
Available for download
Content
Introduction.- Theory in Singularly Perturbed Geometrical Domains.- Steklov-Poincare´ Operator for Helmholtz Equation.- Topological Derivatives for Optimal Control Problems.- Optimality Conditions with Topological Derivatives.- A Gradient-Type Method and Applications.- Synthesis of Compliant Thermomechanical Actuators.- Synthesis of Compliant Piezomechanical Actuators.- Asymptotic Analysis of Variational Inequalities.- A Newton-Type Method and Applications.- The Electrical Impedance Tomography Problem.